In science, we apply Occam's razor. That gives us a hairless cloud decreasing less than linearly with distance from a galactic core.

For fiction, we need not follow Occam's razor. What entities could we multiply?Or, in other words: The map is 90% terra incognita, what dragons could we put there?

My first idea is parallel universes with gravitational interaction. Basically a lot like the parallel universe trope in that the same space holds multiple mostly causally separated realities, the big differences here being that gravity is readily noticeable from all sources and that galactic structure is shared.

Second idea: Normal universe plus fantastic resources. All that exotic matter, unobtainium, and melange your space society needs to work, it's all out there as long as you aren't stuck with lame 21st century detection methods.

Third idea: Alien geometry. Surface area of spherical shells relates to radius from the center of the galaxy in the usual way, density of stars and dust is as it appears to be. Volume contained in a radius is much higher than it would be in a euclidean space. On scales well below that of the galaxy, this means large amounts of weirdness in the shape of space.

The thing about recursion problems is that they tend to contain other recursion problems.

Quizatzhaderac wrote:My first idea is parallel universes with gravitational interaction. Basically a lot like the parallel universe trope in that the same space holds multiple mostly causally separated realities, the big differences here being that gravity is readily noticeable from all sources and that galactic structure is shared.

So gravity works over 4 spatial dimensions, and we can only see the matter in our own universe? That would mean that it drops off with r3 instead of r2, right?

Quizatzhaderac wrote:Second idea: Normal universe plus fantastic resources. All that exotic matter, unobtainium, and melange your space society needs to work, it's all out there as long as you aren't stuck with lame 21st century detection methods.

Great idea. How does the detection method work? High concentrations cause lensing for gravitational waves? What are the limits of that Unonbtanium?Lary Niven, Known Space spoiler:

Spoiler:

The more expensive ships in these books are General Products hulls. They are impervious to anything except massive gravitational shear, massive pressure and a few other items. And "massive pressure" in this case is well beyond containing a hydrogen bomb explosion.There are a few interesting stories about the limits of the material that is so reliable that most people consider it invulnerable.

Quizatzhaderac wrote:Third idea: Alien geometry. Surface area of spherical shells relates to radius from the center of the galaxy in the usual way, density of stars and dust is as it appears to be. Volume contained in a radius is much higher than it would be in a euclidean space. On scales well below that of the galaxy, this means large amounts of weirdness in the shape of space.

AFAIK our space isn't perfectly Euclidean. The angles of a triangle do not add up to exactly 180°. The Pythagoras Theorem isn't exactly accurate. This is because these things assume space is perfectly flat, which it isn't. The difference is immeasurable minuscule on earth but near major masses like super massive black holes it becomes big.You could amplify this effect by a million or a billion. and see where the chips may fall.

Mikeski wrote:A "What If" update is never late. Nor is it early. It is posted precisely when it should be.

My math is admittedly rusty, but is there any geometry that decouples surface area and volume like that (so surface area is no longer the derivative of volume) while still being smooth enough for things to look mostly like our world?

In fact, is there any such geometry at all (whether or not it looks anything like ours)?

Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.---If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

You can have a region of space which, from an observer at infinity, looks like it has a surface area of 4piR^2, with some R, and have the volume inside not be 4/3piR^3 with the same R. Like in a Schwarzschild metric.

This would not at all solve the dark matter issue in any way compatible with known science. Other modifications of GR, like MOND, do change the gravity side of things and get you a solution, in a way that is not very compelling and basically ruled out, but at least not infeasible. These proposals are very much the technobabble labeled magic style. (Which, given the subforum, are all well and good, no shade.)

LE4dGOLEM: What's a Doug?Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Right, but the internally measured radius doesn't match and that's what gives the extra volume.

(Am I correct in believing that if the surface area of a sphere is everywhere 4pi times the square of the internal radius, that's equivalent to saying space is Euclidean?)

Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.---If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

Neil_Boekend wrote:So gravity works over 4 spatial dimensions, and we can only see the matter in our own universe? That would mean that it drops off with r3 instead of r2, right?

I meant "dimension" in the sense of "Krang comes from dimension X; no, I don't know the mathematical definition of dimension, why do you ask?".

A word other than "dimension" is probably needed.

Three spatial dimensions, same as always. Halfway between Sol and Alpha Centari there is another star system that we can't see or touch. Ordinarily we'd only be able to notice it by it's gravity, or maybe neutrino interactions as well. Likewise people from the that phantom system wouldn't be able to see Sol.

How does the detection method work?

I see it mainly as being a bootstrap issue. Once you have it, it's easy to find and work with, but if you don't have it, you're lucky to even know it's there.

I'd say the easiest way is with instruments made with the non-brayonic matter. Maybe have some meta-materials made from combining regular matter and plot-anium, and the meta-material can strongly interact with both.

What are the limits of that Unonbtanium?

That entirely depends on what kinds of unonbtanium one wants in their story. I'd assume most commonly one would want something that explains FTL.

gmalivuk wrote:My math is admittedly rusty, but is there any geometry that decouples surface area and volume like that (so surface area is no longer the derivative of volume) while still being smooth enough for things to look mostly like our world?

Spoilered is an example that doesn't provide much technical information, but I hope helps put one in the right frame of mind.

Spoiler:

Consider the lost woods in the original Legend of Zelda.

It has four entrances, two exits.

Internally it has four (almost identical) screens. As one must travel the correct path in the correct order to reach the west exit.

By contrast, the normal case is each screen has four entrances and four exits. A plus shapes set of five screens has twelve entrances and twelve exists.

As for limiting ourselves to simple topology.

Spoiler:

Consider a rubber sheet. Draw a circle on it and sticks some pins in the circle so it doesn't move. Now manipulate the rubber in the center; poke it pull, fold it, whatever.

Anything you do to stretch the rubber increases the area of the circle, but the circumference of the circle stays exactly the same.

On the scale of 100 AU and less, it would look like our universe the vast majority of the time. This would mean orbital mechanics work as well as the geometry we need to explain all the probes that we have sent. We could add in some exceptions, but they'd need to be very weird to explain why we haven't seen them.

On the scale of 10,000 light years and up, it would look like our universe. This means certain densities of light and gravitational flux at certain radii from the galactic centers. Gravitational flux can't be blocked, so only the surface area and the amount of mass contained therein matters to what gravity is on the surface.Light can be absorbed so the amount of light existing an area depends of what proportion of paths exit an area; so if all of the paths away from a star need to go through a kiloparsec of interstellar gas first, most photons will be absorbed before being captured.

On scales in between, Occam's razor pretty strongly says that space should be roughly flat and topologically simple. But without the razor there's a pretty big space between what we see and what we know. We see a bunch of dots of certain brightness and color and we interpret that as best we can.

The stretched rubber sheet is analogous to the real situation, and my point above was that stretching it like that changes the radius as well as the internal measure (area of the sheet or volume of 3-space). Doogly pointed out that measured from infinit, the radius and surface area can look Euclidean (as can the external view of your rubber sheet), but that depends on the fact that from infinity you get a different value for the radius than what you'd get from the inside.

As for the other analogy, I never played Zelda, but 5 rectangles in a + pattern should have 12 entrances and exits, no? In any case, topological oddities that come from stitching together flat space in weird ways don't really help illustrate something that's supposed to be a smooth transition from small- to large-scale.

(You can of course handwave it bigger-on-the-inside TARDIS styl, I'm just pointing out that there's not a consistent purely geometrical way to get what you want.) - - - There was a 4 or 5-part serial novel in Analog back in the 1990s that posited dark matter as being made from a previously undiscovered set of quark types, and there were aliens made of the stuff. I can't for the life of me remember more details than that, but if someone knows of a list of serialized novels that have appeared in Analog over the years, I could probably pick it out.

Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.---If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

Neil_Boekend wrote:So gravity works over 4 spatial dimensions, and we can only see the matter in our own universe? That would mean that it drops off with r3 instead of r2, right?

I meant "dimension" in the sense of "Krang comes from dimension X; no, I don't know the mathematical definition of dimension, why do you ask?".

A word other than "dimension" is probably needed.

Three spatial dimensions, same as always. Halfway between Sol and Alpha Centari there is another star system that we can't see touch. Ordinarily we'd only be able to notice it by it's gravity, or maybe neutrino interactions as well. Likewise people from the that phantom system wouldn't be able to see Sol.

Yes, we need a different word. I would like to use universe 2 as a name for that place where Krang comes from and where that phantom system is. Our universe would be universe 1. Universe 2 and our universe 1 are in the same 4 spacial dimensional multiverse separated by a distance of only a few mm in the fourth dimensions like sheets of infinitely big paper can be in our 3 dimensional universe. Gravity would be able to influence masses in the neighbouring universe, although mass wouldn't be able to move in the fourth dimension. That would also mean the calculations regarding to how gravity behaves would change, as the real world calculations assume a 3 dimensional space. I'm not sure how stable orbits would be because that's well beyond my skillset.

Mikeski wrote:A "What If" update is never late. Nor is it early. It is posted precisely when it should be.

gmalivuk wrote:but that depends on the fact that from infinity you get a different value for the radius than what you'd get from the inside

Yes, the radius measured from inside starts becoming dodgy when we mess around with the space too much. I suppose it would have been better to draw the distinction between the ratios of the surface area to internal volume, which is what would have mattered in this case.

5 rectangles in a + pattern should have 12 entrances and exits, no?

Right you are, my mistake.

You can of course handwave it bigger-on-the-inside TARDIS style, I'm just pointing out that there's not a consistent purely geometrical way to get what you want

I'm not sure what you mean by "purely geometrical". Any shape one can constructively describable falls within the scope of geometry, no matter how unphysical.

But yes, it would have to be very handwavey, and I can't think of how to accomplish the needed shapes using the type of spacial distortions known to physics.

Neil_Boekend wrote:Universe 2 and our universe 1 are in the same 4 spacial dimensional multiverse separated by a distance of only a few mm in the fourth dimensions like sheets of infinitely big paper can be in our 3 dimensional universe.

I was think more like Gmalivuk's example from the Analog series.

Maybe have copies of the electron, quark, gluon (strong force), and photon (EM) fields. These redundant fields interact with each other and gravity exactly the same as the original, but they do not interact with the original set at all.

So worlds A and B are made from the original and copy particles/fields. The physics of the two worlds are isomorphic, but they can't really see each other.

separated by a distance of only a few mm.....That would also mean the calculations regarding to how gravity behaves would change, as the real world calculations assume a 3 dimensional space.I'm not sure how stable orbits would be because that's well beyond my skillset.

Physics have actually specifically explored this as a solution to the hierarchy problem. Gravitation mechanics on bodies much larger than a few mm would be the same. Below a few mm gravity would be an R^-3 force and classical orbits are impossible. It's reasonable that we've never seen this because gravity is trivial on such scales, and people are only recently checking that active gravity works the same on the mm scale.

On Planck scales the gravitational coupling constant would be about as strong as the other forces'.

That all said, to me that raises the question of why these narratively discrete worlds are separate points in a continuous space.

The thing about recursion problems is that they tend to contain other recursion problems.

The idea of large extra dimensions explaining the hierarchy problem was mulled over for a bit. Basically, what we think of as our universe would really be just a single 3-brane in a 4-D bulk, but whose fourth dimension is less than a millimeter in diameter (but still "large" compared to the extra dimensions usually discussed in string theory). Submillimeter gravitational experiments have since been performed searching for deviations from the inverse square law, and no deviations have yet been found down to ca. 50 microns iirc.

If we were on a 3-brane in a 4-D bulk, then gravity should not be constrained to the brane and would permeate the entire bulk, so on small scales it would decrease as the cube of radius (or higher order if we add multiple extra spatial dimensions). This doesn't exactly solve the hierarchy problem, but it sort of shifts it from a question of why the gravitational constant is so small to why the fourth dimension is so small.

It's not strictly impossible though, and if true, it could kinda-sorta explain dark matter. If there were another 3-brane parallel to ours containing ordinary matter, we would only be able to interact with it gravitationally. However, we would still need to explain why dark matter halos are so diffuse and not shaped anything like the bright matter in galaxies. Also, these 3-branes would be gravitationally attracted to each other, so they should eventually collide. This idea was incorporated into early ekpyrotic models of the universe, with the branes repeatedly colliding an passing through each other in a cycle of Big Bang and Big Crunch. Needless to say, none of this actually matches observation very well at all. But it's fun to think about.

So if we're going 3-branes separated in a fourth spatial dimension, I'd say:

The fourth spatial dimension is 16.16 μm in circumference, looping around. This would make gravity 1% as strong as the weak force on the Planck scale.

There are six 3-branes of roughly equal mass density. Each repels the others due to some currently unknown force. According to the Author's taste this repulsion is overcome at various gravity well depths: either 1) star's cores, 2) neutron/degenerate stars or 3) black holes.

The thing about recursion problems is that they tend to contain other recursion problems.

Eebster the Great wrote: However, we would still need to explain why dark matter halos are so diffuse and not shaped anything like the bright matter in galaxies. Also, these 3-branes would be gravitationally attracted to each other, so they should eventually collide. This idea was incorporated into early ekpyrotic models of the universe, with the branes repeatedly colliding an passing through each other in a cycle of Big Bang and Big Crunch. Needless to say, none of this actually matches observation very well at all. But it's fun to think about.

Therein lies the problem--Dark Matter does not seem to agglomerate into medium-large, dense objects on the scale of planetary or stellar masses. Some black holes MIGHT be made of Dark Matter, since the No Hair Theorem ("black holes have no hair") tells us that a Dark Matter black hole would be indistinguishable from a baryonic-matter black hole, however.

The lack of dense Dark Matter objects tells us that Dark Matter apparently does not possess its own "Dark Electromagnetism"--i.e. an electromagnetic-like interaction between Dark Matter particles. Basically, without such an interaction, there is no way for Dark Matter to emit a "Dark Photon" (which would interact with Dark Matter but not with baryonic matter), which means that a nebula of Dark Matter can not radiate away heat and collapse readily. This inability to collapse also explains why dense baryonic objects (stars, black holes) do not attract individual collections of Dark Matter sufficiently large to throw off our estimate of individual stellar masses as compared to an all-baryonic model.

Right, the dark matter flies towards the center of gravity, then back out the other side. Every bit of dark matter is just flying back and forth indefinitely to create the diffuse halo, with no concern for what it's flying through along the way. That's a simplification of the going theory, at least.

Are there generalizations we can reliably make about the way many-body systems behave only under the force of gravity? I know they can "radiate away" energy eventually gravitationally (over preposterously long time scales), but if we just look at Newtonian gravity, what usually happens? Do some particles get flung away and others cluster in the center? Do they continue to maintain a relatively constant mean distance from the barycenter (averaged over long periods of time)? Is the system so chaotic and variable that we can't make any useful generalizations?